1462 ieee transactions on power systems, vol. 26, no. 3 ...cs.ucf.edu/~qu/journals/ieee power...

1462 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 26, NO. 3, AUGUST 2011

A Self-Organizing Strategy for Power Flow Controlof Photovoltaic Generators in a Distribution Network

Huanhai Xin, Zhihua Qu, Fellow, IEEE, John Seuss, and Ali Maknouninejad

Abstract—The focus of this paper is to develop a distributed con-trol algorithm that will regulate the power output of multiple pho-tovoltaic generators (PVs) in a distribution network. To this end,the cooperative control methodology from network control theoryis used to make a group of PV generators converge and operate atcertain (or the same) ratio of available power, which is determinedby the status of the distribution network and the PV generators.The proposed control only requires asynchronous information in-termittently from neighboring PV generators, making a commu-nication network among the PV units both simple and necessary.The minimum requirement on communication topologies is alsoprescribed for the proposed control. It is shown that the proposedanalysis and design methodology has the advantages that the cor-responding communication networks are local, their topology canbe time varying, and their bandwidth may be limited. These fea-tures enable PV generators to have both self-organizing and adap-tive coordination properties even under adverse conditions. Theproposed method is simulated using the IEEE standard 34-bus dis-tribution network.

Index Terms—Distribution network, network control, powerflow control, PV generators, self-organization.

I. INTRODUCTION

I N recent years, there has been an increasing number of dis-tributed generators (DGs) integrated into the modern distri-

bution network [1]–[3]. Among these DGs, PVs are becomingan increasingly attractive source of renewable energy in certainareas, especially as they become more commercially viable tomanufacture and install [4], [5]. However, the introduction of alarge amount of PV generation could have a negative impact onthe power system at large if the relevant stability and control is-sues are not properly considered.

In a distribution network that contains a high level of pene-tration of PV units but has an insufficient number of storage de-

Manuscript received April 06, 2010; revised April 13, 2010, April 15, 2010,July 13, 2010, and September 09, 2010; accepted September 14, 2010. Date ofpublication October 11, 2010; date of current version July 22, 2011. This workwas supported in part by the U.S. Department of Energy (under the SEGISprogram) and in part by the Florida Energy Systems Consortium. Paper no.TPWRS-00267-2010.

H. Xin is with the Department of Electrical Engineering, Zhejiang University,Hangzhou 310027, China. He was also with the University of Central Florida,Orlando, FL 32815 USA, when he finished this paper (e-mail: [email protected]).

Z. Qu is with the Department of Electrical Engineering and Computer Sci-ence, University of Central Florida, Orlando, FL 32815 USA (e-mail: [email protected]).

J. Seuss and A. Maknouninejad are with the University of Central Florida, Or-lando, FL 32815 USA (e-mail: [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPWRS.2010.2080292

vices, a sudden disturbance (such as the change in sunlight dueto a passing cloud/storm) could trigger a rapid disconnection ofthese PV generators or the reduction of their operating capacity,resulting in a significant loss of active power support. The lossof generation can lead to an array of problems, such as voltagevariation [4], [6], transient stability issues, and even voltage col-lapse [7]–[9], making it desirable to develop a practical and ro-bust scheme of controlling the total output of the PVs, especiallyin the case that the distribution network is weak.

The optimal power flow (OPF) strategy is the standardapproach to dispatch and control traditional generators in thetransmission network [10]–[12]. The strategy has also beenapplied to distribution networks that have a few DGs [13],[14]. These results yield centralized controls by collecting thesystem-wide information and sending the command globally.For a power system whose transmission and distribution net-works have numerous and geographically dispersed DGs, suchcentralized controls are too expensive to be implemented and,even if they could be done, the resulting system is not robust orefficient.

On the other hand, a decentralized control mode, such asthe maximum photovoltaic power tracking (MPPT), constantvoltage and frequency (VF) with droop mode, or the feederpower flow control mode [1], [2], [15], [16], is useful in the dis-tribution network if there are only a few DGs present.

As the level of PV penetration increases, intermittent changesof these PV outputs become too many to enumerate and con-sider, and hence, it becomes intractable for either the decen-tralized or centralized mode to adequately manage a distribu-tion network, such as maintaining the voltage profile. Instead,the practically feasible solution is a distributed control configu-ration [17] that uses local communication networks and hencecombines the positive features of both centralized and decentral-ized controls while limiting their disadvantages. Specifically, aPV generator should incorporate whatever information is avail-able from its neighboring generators or critical nodes into itscontrol law. This distributed control configuration is in line withthe concept that a future smart grid would include communi-cation among network elements [3], [4]. This resulting controlproblem becomes the so-called network control problem whichhas systematically been studied in recent years and also success-fully applied to such fields as cooperative robotic control [18],[19].

The distinctive feature of an appropriately designed networkcontrol is that it admits local and changing communication net-works, is robust with respect to intermittency and latency ofits feedbacks, and also tolerates connection and disconnectionof network components. When a distribution network containsmany groups of DGs whose output may vary in wide ranges,

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XIN et al.: SELF-ORGANIZING STRATEGY FOR POWER FLOW CONTROL 1463

the aggregated power output of all the DGs in each group canbe dispatched and controlled by coordinating the power outputlevel of each DG internally within the given group. For instance,a simple solution to the power-output coordination problem isto prescribe certain utilization profile for all of the PVs in agroup, and the so-called fair utilization profile is that the sameratio of power output versus available power is imposed on allindividual PV generators. In general, the desired control algo-rithm should be able to manage a large number of DGs but re-quire only local information from neighboring units. By doingso, groups of DGs can be formed autonomously based on thepresence of local communication networks, the power in a dis-tributed network can easily dispatched and controlled, and pos-sibly large swings in power outputs of distributed generators canbe tolerated.

In this paper, a self-organizing power control method is pro-posed by applying cooperative control theory of networked sys-tems to power distribution networks. The proposed control al-gorithm can effectively control a large number of PVs which ex-change information among their neighboring units, respectively.The control can make the PVs in one group converge to anygiven utilization profile while providing the desired power beingdispatched from the group. It is distinctive that the proposedcontrol can tolerate the changes in the distribution network, itslocal communication network can be intermittent and have timevarying topologies, and its communication bandwidth can be ofminimum. Typical communication setups are discussed, and thenecessary and sufficient condition for stability and convergenceis also presented.

II. PROBLEM FORMULATION

A. Dynamical Model

Consider a distribution power system network with three-phase inverter-based photovoltaic generators that use the decou-pled d-q control method via phase locked loops (PLL). Underthe d-q frame, the terminal voltage of the th PV generator sat-isfies and , where denotes the magnitudeof the terminal voltage [15]. Thus, output power of the ith PVgenerator can be expressed as

(1)

where and are the output currents in the d-axis andq-axis, respectively; and and denote the active andreactive power.

If an integration control design is pursued for and ,then the dynamics of the distribution system are described bythe following differential-algebraic equations:

(2)

(3)

(4)

(5)

(6)

where (2) and (3) denote the d-loop and q-loop dynamicsthrough which the active and reactive power outputs can becontrolled; variables and are the control inputs to be de-signed; is a vector of an appropriate dimension, and it denotesall the internal network state variables including dynamics ofthe PV generators, loads, and synchronized generators; is avector of algebraic variables in the distribution network suchas the voltages of buses; and (6) is the power flow equation ofthe distribution network.

Controls and are to be designed tocontrol active and reactive power outputs of PV generators sothat the power flow of the network is reasonable. Toward thisgoal, the changes of the PVs’ outputs can be considered to bemuch slower than the dynamics of PVs’ internal variables, andhence, it can be assumed that the dynamics of (4) have beenmade asymptotically stable by their controls. In other words,fast dynamics of can be considered negligible compared to theslowly changing power flow variables. Accordingly, the simpli-fied dynamical models for the distribution network are denotedby

(7)

(8)

(9)

(10)

where , and all the other variables are thesame as those in (2)–(6). In what follows, a distributed cooper-ative control will be designed for system (7)–(10).

B. Problems to be Solved

In a distribution network with many PV generators, its oper-ating condition needs to be adjusted due to many varying factors,such as load and sunlight fluctuations. As was pointed out inthe introduction, it would be impossible to determine and main-tain a feasible operating condition if all of the PV generatorsare independently run under the decentralized control configu-ration shown in Fig. 1(a). The centralized control mode shown inFig. 1(b) is neither practical nor reliable since it requires globalcollection and exchange of information. To handle numerousPV generators in the network, we propose to implement the dis-tributed control configuration as shown in Fig. 1(c).

The basic idea of the proposed distributed control is that, byincorporating local communication networks that share infor-mation among neighboring units, numerous PV generators au-tonomously form a number of generation groups and that eachgroup is represented by a virtual generation unit which aggre-gates all the power generated within. The outputs of these virtualgenerators can be dispatched and controlled by a high-level con-trol (which is equivalent to a transmission and distribution con-trol center). While the latter is similar to the centralized controlconfiguration, the proposed control configuration requires muchless communication since the numerous distributed generatorsdo not communicate with the higher-level control.

Once the power output of each group is dispatched, the pro-posed cooperative control coordinates all the outputs of PV gen-erators in the same group so that, even though the output ca-


Fig. 1. Three different control modes in a distribution network (the dasharrows represent information flow). (a) Decentralized mode. (b) Centralizedmode. (c) Distributed control mode.

pacity of individual PVs may have large swings, a given profileis achieved for their utilization and the sum of their outputs con-verges to the dispatched value. This feature makes it possiblefor all the active PVs to self-organize themselves and be con-trolled. The local information sharing within one group of PVsmay be intermittent, asynchronous, and of varying topology.In other words, the proposed control is robust with respect topossible variations and limitations of communication networks.The utilization profile for PVs in the group can be determinedaccording to such considerations as economic and regulatorypolicies. In what follows, the proposed distributed cooperativecontrol is designed for the case of the fair utilization profile, thatis, that all of the PVs in a designated group are to be run at thesame active and reactive power output ratios. Mathematically,this control problem can be stated as follows.

Problem 1: Design controls and forsystem (7)–(10) such that, at the equilibrium operating point, theutilization profile of PVs is described by the following ratios:

(11)

and

(12)

where is the given output ratio for the ac-tive and reactive power for all the PV generators, respectively;

and are the instantaneous maximum capacity of

and , respectively; and all the are assumed to havethe same sign, and so do all the .

The ratios in (11) and (12) are the utilization percentages ofall the PV units and they are commanded to be the same at thesteady state. Accordingly, the control objective of (11) and (12)is referred to as the fair utilization profile. In general, a distri-bution network can dictate any specific utilization profile. Forinstance, utilization ratio may be desired to converge tofor different . In this case, the designer can introduce the gainof so that the transformed utilization ratio ofneeds to converge to the common ratio . In other words, anyspecific utilization profile can be converted into the fair utiliza-tion profile in (11) and (12) for which the proposed cooperativecontrol is designed. It should be noted that a balanced distribu-tion network is considered in problem 1. If the distribution net-work is unbalanced, the energy management should be differentbecause the output power contains a periodic part resulting fromthe negative current and voltage. For this case, the power in (11)and (12) should be replaced by the positive output power.

By introducing the utilization profile (11) and (12), each ofthe PVs can be controlled by comparing its operation to thatof any or some of its neighboring units, and there is no need forevery PV unit to communicate with every other unit or the high-level control. Accordingly, the proposed distributed control foreach PV generator is of the general form

(13)

where denotes the output of the high-level control; rep-resents the output of the th PV generator (for );

is the matrix defined below to describe the instanta-neous communication topology:

......

. . .

(14)

In (14), for all ; if the output of theth PV generator is known to the th PV generator at time ,

and if otherwise; if the th PV gener-ator receives information from the high-level control at time ,and if otherwise. As shown in Fig. 1(c), the pro-posed control utilizes certain neighboring information but doesnot assume any global information. In the extreme case thatthe high-level control collects information from and sends com-mand to all the PVs, matrix S in (14) has 1 as its entries in thefirst column, and the corresponding control becomes the central-ized control configuration in Fig. 1(b). The other extreme caseis that none of the PVs exchange information with each otheror the high-level control, then matrix S has entries forany , and the proposed control reduces to a decentralizedcontrol.

The specific expression of the control (13) will be synthe-sized in Section IV-A. In both the control (13) and matrix S of(14), the identity of means that the control at every PVgenerator can and should utilize its own output as one of the


feedback. Whether or not the high-level command or informa-tion from other PV generators is available at the th generatoris determined by the current status of its communication net-work represented by the th row of communication matrix .Intuitively, it would be sufficient for all the PV generation unitsto be controlled properly if each of the PVs can receive someinformation from some of its neighboring units and if the com-mand of the total dispatched power is sent to some of the PVsin a group. This brings out the problem of determining the min-imum information sharing that must exist among the group ofPV generators and between the group and the high-level con-trol. That is, the requirement on communication network needsto be specified to ensure the proposed distributed control wouldwork, and it is stated as the following problem.

Problem 2: Determine how the local communication networkamong the PVs (the matrix) should be designed in order to en-sure efficiency and reliability of the network while minimizingeconomic costs.

It should be emphasized that the proposed distributed controladmits time varying, intermittent, and asynchronous communi-cation networks. In fact, given any limited bandwidth of onecommunication node, it would be better for the convergence ofnetworked control that the node sends its information intermit-tently to different nodes in its vicinity. This means that, in (14),communication matrix is time-varying in general or, moreprecisely, piecewise constant. Specifically, consider

(15)

which means that changes at , or simply,for . The time-varying nature of

matrix S also implies that the proposed distributed control hasinherent robustness against interruptions, data loss, and otherphenomena of a typical communication network.

Problem 2 defined above arises naturally from the fact thatboth the communication network topology and the availabilityof PVs are time varying. In addressing the problem, we aim tofind a simple condition on feasible and convergent sequencesof . The basic rule for designing appropriatelocal communication topology will further be discussed inSection IV. Through such a design of local communicationnetwork, the candidate sequences of can bechosen to ensure the convergence of the distribution networkunder the proposed control. Due to the time-varying natureof local communication networks and their resulting coop-erative controls, the resulting closed loop system around theequilibrium point is piecewise-constant, and its stability has tobe analyzed in terms of convergence of matrix sequences. Inother words, the proposed control can be designed by using thestate-of-the-art approach from cooperative control of networkedsystems rather than traditional methods such as eigen-analysisand pole placement.

Upon the solutions to Problems 1 and 2 being found, all thePVs are organized into a number of groups and, within eachgroup, the PV generators are controlled to satisfy the givenutilization profile. Accordingly, each group of the PVs canbe viewed as a virtual generator of a larger capacity and with

an aggregated output. The aggregated outputs of these virtualgenerators would be dispatched and in turn the operating ratiosin group’s utilization profiles are determined, which resultsin much less long-distance communication and also a muchsimpler design for a high-level control [see that in Fig. 1(c)]to address ancillary service issues, given the large numbers ofPVs in the distribution network.

Thus, depending upon the needs of the particular distributionnetwork of our concern, the high-level control can be designedaccording to one of several objectives. Among the possibilities,the high-level control can be designed to be either a balancedgenerator in the islanding operation, or a virtual power plantfor load management [20], or a smart agent for maintaining fre-quency or a desired voltage profile [1], [6], and so on. Rele-vant to this paper is the study in [21] where the power at thefeeder is kept constant such that all the rest of the load demandsare picked up by DGs. In this case, the feeder becomes a trulydispatchable load from the utility side, allowing demand-sidemanagement arrangements. In this paper, the idea of makingthe load constant to the utility grid is extended; in particular,the high-level control is designed so that the reactive power iscontrolled to support the voltage at some critical bus and to keepthe active power consumed by loads in an area or at a feeder tobe constant. This leads to the third problem to be solved in thepaper.

Problem 3: Based on the solutions to Problems 1 and 2, de-sign a high-level control [as shown in Fig. 1(c)] for the system of(7)–(10) such that, for each group of PVs, the voltage of a crit-ical bus is of a specific value and the active power flow acrosscertain transmission line is of a fixed amount. Namely, the fol-lowing set points are achieved at the equilibrium:

(16)

(17)

where and are the given reference values; andrepresent the voltage of the selected bus and the active

power over the chosen transmission line, respectively. Note that,in (16) and (17), variables and are functions of theoutputs of PVs and, for simplicity, the functional dependence isdenoted by .

Several observations are worth making here regarding theaforementioned design problems.

1) The design problems 1–3 are defined explicitly in termsof dynamics of PV generators, and they can be extendedby incorporating dynamics of other types of DGs. That is,for a distribution network with other types of DGs suchas wind generators, the same design problems can be for-mulated and solved for energy management. As argued in[21], a hierarchical control architecture should be used tocontrol the distribution network with many DGs. In this re-gard, Problem 3 is the high-level control, Problems 1 and2 are the middle-level control within each of the groupsof DGs, and also there are low-level individual controls[which are already embedded into (7)–(10)] at each of theDGs to control the individual output. To apply such, theDGs can easily be classified into groups according to their


location and proximity, for instance, at a feeder, within acommunication zone, solar/wind farms, etc. How to bestpartition DGs into groups is an important problem, but itis out of the scope of this paper. In our simulation study,all the PVs connected to the same feeder are considered tobelong to one group.

2) In Problems 2 and 3, a DG group is controlled to act as avirtual FACTs element supporting the voltage of a criticalbus. In general, it is difficult to determine the critical busfor a large-scale power system. The common practice is bysimulations or by experience. For a radial distribution net-work, existing simulation studies [2], [6] have shown thatthe bus at the end of a feeder is typically the one subject tovoltage violation when power from DGs changes intermit-tently. Thus, in our simulations, the end bus of a feeder ischosen to be the critical bus.

3) Problem 3 aims to coordinate any given DG group withthe overall power grid. The desired active and reactivepower output (i.e., reference values and ) ofthe PV group can be determined by either offline or on-line optimization approach or by one of the market-basedapproaches [6], [13], [22]. Once and are ob-tained, the extended power flow equations of (6) and of(16) and (17) could be used to determine the group’s aggre-gated power output (which in turn yields the actual outputratios of the active and reactive power, and ). Ifthe high-level control could collect enough information(including the parameters of the power system networkwith virtual DG generators), the desired output ratios ofevery PV group can be calculated directly. Otherwise, thehigh-level control for system coordination needs to be de-signed as prescribed in Section IV-B.

III. RULE OF COMMUNICATION TOPOLOGY DESIGN

As outlined in the previous section, the topology of thelocal communication network among the PVs in one groupcan be intermitted (time varying) and asynchronous, in whichcase the communication matrix describing the topologybecomes piecewise constant. To ensure that a given utilizationprofile is achieved among one group of PVs, there need to belocal information sharing among the DGs. Heuristically, themore communication channels there are, the more informationpropagates within the group, and the faster the convergenceto the desired utilization profile. However, this quickly be-comes an uneconomical solution to the problem. It followsfrom cooperative control theory [23] that the minimum re-quirement on the communication topologies is the so-calledsequential completeness condition. Mathematically, this re-quirement is that the sequence of communication matrices

be sequentially complete in thesense that, over an infinite sequence of finite consecutiveintervals, the composite graph over each of the intervals (orthe binary product of all the matrices of S over the interval)has at least one globally reachable node (in the sense that allother nodes can be reached from the globally reachable nodeby following the directed branches of the graph) [23]. Thus,for the purpose of distributed control design, the following

Fig. 2. Sample graphs of communication topology. (a) Existence of one glob-ally reachable node. (b) Absence of globally reachable node.

rule is given for designing local communication networks andscheduling local communications.

Rule: Communication matrix S is piecewise constant, and thecorresponding sequence is sequen-tially complete.

The above sequential completeness condition is a very pre-cise method to schedule local communication, and it is alsothe necessary and sufficient condition for any properly-designedcooperative system to converge [18], [23]. A more restrictive(sufficient but not necessary) condition is that the compositegraph is strongly connected (which implies that, by followingthe directed branches, every node can be reached from any othernode). To illustrate its application, consider communication ma-trix and construct the corresponding graph by linking thenodes according to nonzero entries in . One can easily deter-mine whether the resulting graph has at least one globally reach-able node or not. For instance, consider the graphs in Fig. 2.Fig. 2(a) has node 0 as the unique globally reachable node; andnone of the nodes in Fig. 2(b) is globally reachable because thereare two isolated groups of nodes.

The above general method can be used to verify or establishthe sequential completeness condition, and the details can befound in [18] and [23]. In designing distributed control for PVsin a distribution network, we choose to focus our attention to thefollowing very special case of local communication topology: Ifmatrix has at least one globally reachable node for every

, then sequence is guaranteed to be sequentiallycomplete. The following example further explains this specialcase for the sequential completeness condition. Consider a ma-trix sequence defined by for

where , 1, 2 and is an integer:

Fig. 3 plots the graphs corresponding to those communicationtopologies. It follows from Fig. 3 that the information can prop-agate from node 0 to nodes 1, 2, and 3. Therefore, all of thecommunication matrices are complete by themselves, and so aretheir sequences.

While not necessarily required, this special case can be usedto design and implement a redundant local communicationnetwork which satisfies the so-called rule of “N-n”. Namely,


Fig. 3. Graphs for time-varying communication topologies.

when n communication channels cannot work properly in someamount of time, the communication matrix corresponding tothe remaining communication channels should be kept to becomplete. It should be also noted that the convergence rateof the closed loop system depends upon connectivity of thecommunication network, so it is important to design a reason-ably connected local communication network within certainphysical and economic constraints.

IV. COOPERATIVE CONTROL STRATEGY

A. Control Strategy for Fair Utilization

In this subsection, the high-level control is assumed to havesufficient information, such as the exact parameters and the (ag-gregated) states of the distribution network, so that the desiredoutput ratios and can be computed directly using the ex-panded power flow equations. This assumption will be removedin the subsequent subsection.

It follows from (7)–(9) that

(18)

(19)

The cooperative control laws for the th PV generator are

(20)

(21)

where and are the gains

(22)

and is the generic entry of matrix defined in (14) for .Similarly, can be defined for and is its generic entry.

Without loss of any generality, let us choose for simplicitythat

(23)

Then, it follows from (18)–(21) and (23) that the closed loopsystem becomes

(24)

(25)

The following theorem shows that, if the PV generators arecontrolled by (20) and (21), their active and reactive power uti-lization profiles converge to the desired values defined in (11)and (12), respectively.

Theorem 1: Consider control laws (20) and (21) and supposethat the communication rule is satisfied among the PVs. Then,the output ratios of their active and reactive power converge uni-formly and asymptotically to the common values of and ,respectively.

Proof: System (24) can be rewritten as

(26)

where . On the other hand, constant is thetrajectory of the following virtual system:

(27)

Therefore, stability of system (26) is identical to that of the fol-lowing extended system consisting of (26) and (27):

(28)

It follows from [23, theorem 5.4] that, if communicationmatrix defined by (22) is sequentially complete, system(28) uniformly asymptotically converges to , where

and is the constant determinedby the initial state and topology changes. It follows from

that . Thus, uniformlyasymptotically converges to . Similarly, reactive powerratios also converge to the common value of .

Theorem 1 provides the solution to both Problems 1 and 2.The salient features of the proposed distributed control havebeen described in Sections II and III, and they will be illustratedin Section V.


Fig. 4. Control for determining the desired ratio of Q.

Fig. 5. Control determining the desired ratio of P.

B. Control Design for System Coordination

Since the high-level control may not have enough informa-tion to determine the desired utilization ratios, we propose thefollowing distributed control (also shown in Fig. 4) to adjust thereactive power ratio:

(29)

where is the critical bus voltage of interest; is the up-dated value which is used as the input for (25); andis an input for achieving additional objectives (to be explainedshortly). In parallel, the active power control over a specifiedtransmission line is controlled according to Fig. 5 and as

(30)

where is the desired active power over the given transmis-sion line; is the resulting utilization ratio that drives (24); and

is an input for other considerations. Intuitively, thephysical meanings of controls (29) and (30) are that, if the busvoltage (or real power transmission) is less than its referencevalue, the proposed distributed high-level control is to commandsome of the PVs (through its local communication network) toincrease their reactive (or real) power ratio and that the rest ofPVs will also cooperate toward the same goal under their dis-tributed cooperative controls. Hence, an increase of in (30)should result in an increase of until reaches its de-sired reference value of .

Combining (20), (21) and (29), (30) yields the complete setof distributed control laws:

(31)

Mathematically, by choosing gains and to be smallenough, then the desired utilization issued by the high-level con-trols changes much slower than the outputs of the PVs. It isknown [23] that the system in the form of (28) is exponentiallyconvergent to and it is robust with respect to any distur-bance in terms of for every pair of . Accordingly,[23, theorem 5.4] can be used to conclude that, due to the separa-tion of time scales, system (24) and (25) remains to be asymptot-ically convergent (to the common desired utilization ratios) andso is the closed loop system under the entire set of distributedcontrol (33). This result provides the solution to Problems 1, 2,and 3.

The following two remarks are worth noting about the dis-tributed high-level controls. 1) PVs can also be used to damppossible oscillations existed in a power system network or to im-prove the long-term stability by designing the additional controlinputs and (shown in Figs. 4 and 5)in a way similar to the PSS and AVR controls for synchronousgenerators. This subject will be studied in future research, butin this paper, these additional inputs are set to zero. 2) Thehigh-level controls can also be implemented discretely, that is,the following updating laws can be used instead:

(32)

(33)

where and are the step sizes in adjusting the utilizationratios; is the standard sign function; .are the time instants of updating.

C. Further Discussions on Distributed Control

In addition to the distinct features already described inSections II and III, the following observations are also worthnoting about the proposed distributed controls.

1) In the distributed controls, is assumed to benonzero. In the event that some of the PV generatorsare out of service (due to weather or otherwise), theapparent singularity of can be avoidedby using the simple rule that, if , the thcolumn of communication matrix S is set to zero. Thatis, a PV generator in any group is ignored unless it hasmeaningful power generation capacity.

2) It has been shown that is not required forall the PVs. This means that the interaction between thedistributed high-level controls and distributed coopera-tive controls can also be intermittent and time varying. Inparticular, when the dispatched power over certain trans-mission lines is changed or critical bus voltages are ad-justed, only their reference values in the high-level con-trollers need to be modified.

These two features imply that the proposed two-level dis-tributed controls are very flexible and effective, which enablethe groups of PVs to be truly self-organizing according to their


Fig. 6. Diagram of the IEEE 34-bus network.

capacity and local communication networks. Should more pathsbe added into the local communication networks, the faster thesystem converges, which will be illustrated in the simulationstudy.

V. SIMULATION STUDY

In this section, the standard IEEE 34-bus distribution networkis used to illustrate effectiveness of the proposed distributedtwo-level controls. The network has its main voltage at 24.9 kV.Its topology is shown in Fig. 6. Its DGs include 16 PV genera-tors and one gas turbine generator. Simulations are done usingDigsilent, and balanced distribution networks are considered.

The parameters of the system can be founded at the link http://ewh.ieee.org/soc/pes/dsacom/testfeeders.pdf. Basic operationalconditions, dynamical models, and other settings are:

PV parameters: The initial maximums of active and reac-tive power are set to 1 MW and 1 MVAR, respectively.Loads: . Their model is com-posite (a dynamical part and a constant impedance part of50% each).Gas turbine generator: Its active power is 2 MW andthe terminal voltage is set to 1.0 p.u.; the default model

in Digsilent is used with IEEE Type 1 control for AVR,PSS_ostab1 model for the PSS, and the IEEE-G1 modelfor the governor.PV generators: .External grid: An infinite bus (1.0 p.u.).The parameters in the aforementioned dynamical modelsare included in the Appendix.High-level controls: The voltage is controlled for the crit-ical bus to which PV 1 is connected (recall that, as dis-cussed in Section IV, the last bus in a feeder is typicallychosen for a radial network with intermittent DGs); activepower control is to keep a constant amount of power movedownstream of the feeder (line 1 and its positive directionare shown in Fig. 6).Matrix of communication topology: The local commu-nication network is represented by matrix S in (34) where

denotes the ith PV generator and isthe high-level controller (which coordinates the aggregatedpower and hence is considered to be a virtual PV generatorin the lead). Unless mentioned otherwise, matrix S of (34)is the one used in the simulation:

......

......

.... . . ...

(34)

As specified by (34), the 1st and the 2nd PV generatorsreceive the information from the high-level control; gener-ators G1, G2, G3, and G6 are closely coupled, and the restof generators follow G2 up to G6 by receiving informationfrom them.

It is easy to verify that the aforementioned communica-tion topology satisfies the communication rule presented inSection III. In fact, the communication topology is intentionallychosen to be redundant so that, if some of the entries in matrixS were to switch from 1 to 0 intermittently, the communicationrule should still be observed unless many of the communicationchannels stop working at the same time. This shows that thelocal communication network can be designed to be robust.

In this distribution network, the distributed generators (in-cluding the gas turbine generator) provide power to not onlythe local loads but also the external main grid. In the simula-tion, total penetration levels of DGs and PVs are to be increasedup to about 360% and 220%, respectively. The correspondingvoltages at the PV terminal buses are shown in Table I with dif-ferent PV penetration levels (provided that all the PVs are runaccording to the fair utilization profile and their power factorsare also kept to be same). From this table, one can see that, ifthe penetration level of PVs is raised further, the bus voltage


TABLE IPVS’ TERMINAL BUS VOLTAGE FOR DIFFERENT LEVELS OF PV PENETRATION

shall go out of the feasible range (0.9 p.u.–1.1 p.u.). Thus, un-less being controlled appropriately, operations of this systemwill have voltage problems under certain disturbances.

The subsequent simulation study is to verify that, under dis-turbances and interruptions, the proposed distributed two-layercontrol can make the system operate well and all the PV gener-ators’ outputs converge according to the desired utilization pro-file. The following cases are simulated:

1) short-circuit faults;2) changes in sunlight;3) load changes and intermittent communication interrup-

tions.

A. Dynamic Responses to Short Circuit Faults

The fault location is labeled by point (a) or the associated reddot in Fig. 6. The fault at point (a) occurs at 0.0 s and is clearedafter 0.12 s. The resulting dynamical responses of the networkare shown in Fig. 7.

Fig. 7 shows that the system is asymptotically stable underthis fault and the corresponding time scales are in seconds. Incomparison, dynamics of internal state variables such as thoseof synchronized generators are much faster than the changes inPV generators’ outputs. This validates the assumption (made inSection II) that, for the power control problem, those internaldynamics can be ignored.

It can also be observed that, at the time that the fault oc-curs, the active power generated by the PV generators decreases,and so does the active power across line 1. Accordingly, thehigh-level control commands PV 1 and PV 2 to increase theirpower output ratios and, as the result of the proposed cooper-ative control, all the rest of PV generators follows. At the end,all the PV generators asymptotically reach the fair utilizationprofile. This transient process is plotted in Fig. 7(3). Reactivepower is controlled in a similar way, as shown in Fig. 7(4).

B. Dynamic Responses to Rapid Changes in Sunlight

Next, sudden changes of available power due to weather con-ditions are considered. In the simulation, the maximum activepower capacity of PV 1, PV 3, and PV 5 are to vary between10% and 100%, as shown in Fig. 8(1).

Fig. 7. Dynamic responses under fault (a): (1) Frequency of gas-turbine gener-ator. (2) Angle of the gas-turbine generator. (3) Active power output ratios forPV generators 1 to 4. (4) Active power output ratios for PV generators 1 to 4.(5) Critical bus voltage. (6) Active power transmitted over line 1.

Fig. 8 shows the dynamical responses of the system. Inparticular, the active/reactive power output ratios are shownin Fig. 8(2) and (3), respectively; and the power transmittedover line 1 and the bus voltages are plotted in Fig. 8(4) and (5),respectively.

When the sunlight reaching a PV generator starts to decrease,the active power output ratio initially increases since the max-imum available power of the corresponding PV generator is de-creased. This process is apparent in Fig. 8(2) and (3) in whichthe active power output follows the trend of changes in sunlightexcept for the transient responses due to the aforementionedreason and to the controls.

As sunlight changes, the distributed cooperative controlmakes PV output ratios converge to new operating points de-termined by the distributed high-level controls. The high-levelcontrols do not know the current generation capacity of all thePV generators since they communicate only with PV generators1 and 2. Nonetheless, during the whole period of system opera-tion, the active power sent over line 1 and the bus voltages aremaintained around their designated values, which are shownin Fig. 8(4) and (5). This confirms the features claimed in theprevious discussions.

Under the proposed power flow control method, the feedercan be considered from the viewpoint of bus (b) to be a virtualemulated load of constant active power, and the inner voltage ofthis feeder can be controlled by reactive power control of the PVgenerators. Fig. 9 shows the changes of real and reactive poweroutput ratios. Therefore, the effects due to the fluctuations of the


Fig. 8. Responses under sunlight changes: (1) Sunlight changes. (2) Activepower outputs of PV generators 1, 2, 3 and 5. (3) Reactive power output ratiosof PV generators 1, 3, and 5. (4) Active power across line 1. (5) Voltages at thecritical buses. (6) Rotor angle of the gas-turbine.

Fig. 9. Responses to sunlight changes: (1) Active power ratios of PV 1, PV 3,and � . (2) Reactive power ratios of PV 1, PV 3, and � .

PV real power generation can be reduced or minimized by im-plementing local information sharing and cooperative controls.It is believed that the proposed method can be applied to solvevoltage regulation problems.

C. Load Changes and Communication Interruptions

The previous simulations show that PV generators can au-tonomously adjust their outputs to converge to a prescribed uti-lization profile (i.e., the fair utilization profile). In what follows,a case is studied to show that the proposed control also has

Fig. 10. Intermittent interruptions in communication channels.

Fig. 11. Responses to load changes with and without intermittent communica-tion.

strong robustness against communication interruptions and loadvariations.

Consider the following severe case that local communica-tion network is interrupted intermittently and the loads varysimultaneously.

1) The simulated communication interruptions are chosen asfollows: the communication channels of ,

, and are intermittent, and the time instantsof their changes are random [whose changes are shownin Fig. 10(1), in which “1” means that the correspondingchannel is working and “0” otherwise).

2) All loads ramp to 200% of the base levels within 1 s, and10% loads of the base loads are cleared at 5 s and 10 s,respectively.

Dynamical responses of the gas-turbine generator and the PVgenerators are shown in Fig. 11, in which the dashed and solidtrajectories represent the results without or with communicationinterruptions. The output ratios of representative PV generators


Fig. 12. Responses to intermittent communication and load changes. (1) Activepower ratios of PVs 1–3. (2) Reactive power ratios of PVs 1–3.

(PVs 1–3) are plotted in Fig. 12. As expected, we see by com-paring solid and dashed trajectories that convergence is fasterwithout communication interruptions.

VI. CONCLUSION

A distributed two-level control scheme is proposed for powercontrol of groups of PV generators in a distribution network.The proposed control guarantees that the distribution networkcan autonomously adjust itself to a feasible operating point(after disturbances occur) and that all the PV generators in onegroup converge to a prescribed utilization profile. The proposedcontrols require only intermittent information sharing amongneighboring generators, and topologies of local communicationnetworks can be time varying. As long as the communicationnetworks meet the minimum information exchange require-ment (of the matrix sequence being sequentially complete),the proposed controls ensures convergence. Simulations ofthe IEEE benchmark distribution network are used to validatethe features and effectiveness of the proposed method. Theproposed design methodology is also applicable to distributionnetworks with different types of DGs including solar-, wind-,and ocean-energy power generators.

APPENDIX

The parameters for the gas turbine generator are:, , , ,

, , , ,, .

The AVR model in the gas turbine generator is the IEEE type1 [24]. Its transfer function is shown in Fig. 13 and the parame-ters are: , , , ,

, , , ,.

The PSS in the gas turbine generator is the PSS_ostab2 modelprovided by the Digsilent. The transfer function is shown inFig. 14, in which the parameters are: ,

, , , ,, , ,

Fig. 13. Transfer function of IEEE-1 exciter.

Fig. 14. Transfer function of PSS-ostab2.

Fig. 15. Transfer function of Gov-IEEEG2.

Fig. 16. Transfer function of load dynamics.

, , .

The governor in the gas turbine generator is the IEEE-G2model, the transfer function is shown in Fig. 15, and the param-eters are: , , , ,

, .The parameters for the PV generators are: ,

, , .The dynamical model for the loads is shown in Fig. 16, and

the parameters are: , ,, , .

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Huanhai Xin was born in Jiangxi, China, in 1981.He received the Ph.D. degree from the Depart-ment of Electrical Engineering, Zhejiang Univer-sity, Hangzhou, China, in June 2007.

He is currently an Associate Professor in theDepartment of Electrical Engineering, ZhejiangUniversity. He was a post-doctor in the ElectricalEngineering and Computer Science Departmentof the University of Central Florida, Orlando,from June 2009 to July 2010. His researchinterests include power system stability analysis

and renewable energy.

Zhihua Qu (M’90–S’93–F’09) received the Ph.D.degree in electrical engineering from the GeorgiaInstitute of Technology, Atlanta, in June 1990.

Since then, he has been with the University ofCentral Florida (UCF), Orlando, currently a Pro-fessor and Interim Chair of Electrical and ComputerEngineering and the SAIC Endowed Professor ofUCF. His areas of expertise are nonlinear systemsand control, energy and power systems, autonomousvehicles, and robotics. In energy systems, his re-search covers such subjects as low-speed power

generation, dynamic stability of distributed power systems, anti-islanding con-trol and protection, distributed generation and load sharing control, distributedVAR compensation, distributed optimization, and cooperative control. Dr. Quis the author of three books: Robust Tracking Control of Robot Manipulators(Piscataway, NJ: IEEE Press, 1996), Robust Control of Nonlinear UncertainSystems(New York: Wiley, 1998), and Cooperative Control of Dynamical Sys-tems with Applications to Autonomous Vehicles (New York: Springer-Verlag,2009).

Dr. Qu is currently serving on the Board of Governors of the IEEEControl Systems Society and as an Associate Editor for Automatica, IEEETRANSACTIONS ON AUTOMATIC CONTROL, and the International Journal ofRobotics and Automation.

John Seuss received the B.S. degree in electricalengineering from Georgia Institute of Technology,Atlanta, in 2006. He is currently pursuing theM.S.E.E. degree at the University of Central Florida,Orlando.

His research interests include power system sta-bility analysis and control.

Ali Maknouninejad received the M.S. degree fromthe Iran University of Science and Technology. Cur-rently, he is pursuing the Ph.D. degree at the Univer-sity of Central Florida, Oralndo.

His research interests include inverter design andcontrol.

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